To conclude, (REF ) also implies the following quasi-ergodicity property, as shown in [1]} [ou autre
référence de William ? Le papier sur (E') ?] (see also [2]}, [3]}): for all
measurable function \(f:E\rightarrow [-1,1]\)  and all \(x\in E\)  and \(n\ge 1\) ,
\(\left|\mathbb {E}_x\left[\left.\frac{1}{n}\sum _{k=0}^{n}f(X_k)\ \right|\ n<\tau _\partial \right]-\int _{E}f(x)\eta (x)\nu _\text{QS}(dx)\right|\le \frac{C^{\prime \prime }}{n}\) 
